The correct term for a variety of activities aimed at serving the public, such as schools and shops, is "public services." Public services encompass essential functions provided by the government or private entities that aim to benefit the community. These include education, health care, public safety, transportation, and many other services that are vital for societal functioning and public welfare.
Local services, while similar, typically refer to services that are specific to a certain area or community and may include smaller, more localized operations. Community centers focus on providing recreational and social opportunities to residents but do not encompass the broader range of services described in the question. Social infrastructure is a more abstract term that could refer to the underlying structures that support social activities, but it is not as specific as public services regarding what the question describes. Thus, public services is the most accurate and comprehensive answer to the question posed.